Agnès,
There are a couple of things that are going to make this easy vs. very hard.
1. How big is the change? <1std is hard
2. How many points before and after the suspected change? 25-30 is great, less than that, combined with a small shift and the signal to noise ratio starts to get small.
There are lots of approaches to this problem. The easiest is to just use the Tests in the control chart platforms.
The next easiest approach is to use the Partition platform. Put the time variable in the X role and your measured response in the Y role. Interactively split the data to find segments of time with different means. With this approach, when I have lots of splits, its a good idea to be skeptical of segments that are short, and splits with small log worth score where the difference in the mean is small.
The multivariate control chart's change point analyzer is nice, but it can only find one change point. Then you have to manually partition the data and repeat the change point on each of the following partitions.
JMP Systems Engineer, Health and Life Sciences (Pharma)